Right triangle

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A typical right triangle

A right triangle (or right-angled triangle, more commonly in British English) has three sides, with an angle that equals 90º - that is, a right angle.

The general right triangle is the subject of one of the more famous mathematical ideas, the Pythagorean Theorem. It states that the sum of the squares of the legs (short sides) of a right triangle is equal to the square on the hypotenuse (the long side, opposite the right angle). Using the figure to the right, this means:

The analysis of ratios between sides of right triangles with hypotenuse = 1 is at the heart of trigonometry. The sine of the angle at A is determined as the ratio of a/c, the cosine as b/c and the tangent as a/b. Relative to the angle A, the side b is described as the adjacent side and a as the opposite side.